As one of many time-bending series on right now, Legends of Tomorrow has a difficult task. In addition to balancing a group of superhero characters, it also needs to sprinkle its ensemble throughout time. That's why there are multiple answers if you ask, who is Commander Steel on Legends of Tomorrow? There have been two versions of the character on the series already, which makes sense, because the Commander was originally written in DC Comics as a legacy hero whose mantle has been passed down from father to son a few times.
In the comics, the Commander/Captain Steel identity belonged to family members Henry Heywood, Hank Heywood III, and then Nathaniel Heywood. And the New 52 version of the character, Hank Heywood, Jr., changed canon when he was written as a Filipino-American taking on the Citizen Steel mantle.
But the Heywood name should be familiar to Legends fans, because both versions of the character on the show have that surname. In the 1940s, the original Justice Society of America version of the character is indeed Henry Heywood, while the contemporary rendition is his grandson, Nate Heywood. Many of the Legends biographical details are changed from the original canon in order to make The CW's take on it a little more unique, but the names and general time periods are the same.
One major difference from the comics is making Nate a historian with an expertise in the 1940s and WWII, the exact period when his grandfather originally became Commander Steel. In the comics, as a former college athlete forced to get an amputation, Nathaniel receives his powers after being attacked by a Nazi group called "The Fourth Reich," while on the show, he grew up as a sheltered hemophiliac who can't engage in physical conflict, retreating into his love of history.
I suppose making Nate a WWII expert obsessed with studying the past is a way to tie him to his grandfather's legacy, because in Legends of Tomorrow and in the comics, the original Commander Steel is a Captain America-esque supersoldier, transformed with the aid of steel enhancements after an injury.
The other Legends are woven into Nate's LoT and Arrow origin story as well. Eobard Thawne's scientific experiments and the Atom's choice to inject them into Nate are responsible for his transformation. After the injection, Nate's biology changed, making his bones and flesh into a unique, steel-like alloy. In the past version, his grandfather was simply armed with a gun and a super suit, not completely changed, like his son.
Legends of Tomorrow has played a bit with Commander Steel, and the upholder of his legacy, Captain Steel, but overall, it's just a slight twist on these classic DC Heroes.